Review question

# How are the sums of $n$, $2n$ and $3n$ terms connected here? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8493

## Suggestion

1. If $S_1$, $S_2$ and $S_3$ are the sums of $n$, $2n$ and $3n$ terms of an arithmetic progression, show that $S_3=3(S_2-S_1)$.

Is there a formula for the sum of the first $n$ terms of an arithmetic progression that we could use?

1. Find the sum of $n$ terms of the series $1+\frac{3x}{(1+2x^2)}+\frac{9x^2}{(1+2x^2)^2}+\frac{27x^3}{(1+2x^2)^3}+....$ For what values of $x$ does this series have a sum to infinity?

What kind of series is this? When does this kind of series have a sum to infinity?